Digital tools for analyzing nondiffeomorphic shapes
The Euler Characteristic Transform (ECT) of Turner et al. provides a way to statistically analyze nondiffeomorphic shapes without relying on landmarks. In applications, this transform is typically approximated by a discrete set of directions and heights, which results in potential loss of informatio...
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| Veröffentlicht in: | Proceedings of the National Academy of Sciences - PNAS Jg. 122; H. 46; S. e2426574122 |
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| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
United States
18.11.2025
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| Schlagworte: | |
| ISSN: | 1091-6490, 1091-6490 |
| Online-Zugang: | Weitere Angaben |
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| Zusammenfassung: | The Euler Characteristic Transform (ECT) of Turner et al. provides a way to statistically analyze nondiffeomorphic shapes without relying on landmarks. In applications, this transform is typically approximated by a discrete set of directions and heights, which results in potential loss of information, as well as problems in inverting the transform. In this work, we present a fully digital algorithm for computing the ECT exactly, up to computer precision; we introduce the Ectoplasm package that implements this algorithm, and we demonstrate that this is fast and convenient enough to compute distances in real-life datasets. We also discuss the implications of this algorithm to related problems in shape analysis, such as shape inversion and subshape selection. We also show a proof-of-concept application for solving the shape alignment problem with gradient descent and adaptive grid search, which are two powerful methods, neither of which is possible using the discretized transform. |
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| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 1091-6490 1091-6490 |
| DOI: | 10.1073/pnas.2426574122 |